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Zbl 0992.92035
Nelson, Patrick W.; Perelson, Alan S.
Mathematical analysis of delay differential equation models of HIV-1 infection. (English)
[J] Math. Biosci. 179, No.1, 73-94 (2002). ISSN 0025-5564

Summary: Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells, $\delta$, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of $\delta$. We also provide some general results on the stability of non-linear delay differential equation infection models.

MSC 2000:: *92C60 Medical epidemiology
34K20 Stability theory of functional-differential equations
92C50 Medical appl. of mathematical biology
92D30 Epidemiology

Keywords: HIV-1; delay differential equations; combinationantiviral therapy; T-cells

Cited in: Zbl 1260.92065

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